# Resonance/energy levels contributing structures

• DDTea
In summary, Robert B. Grossman discusses resonance in the context of the Schrodinger equation. He defines it as a degenerate solution of equal energy, and explains that it is not limited to structures of the same energy. The concepts should be exposed in books by Linus Pauling or Eyring Walter and Kimball.
DDTea
I'm working my way through The Art of Writing Reasonable Organic Reaction Mechanisms by Robert B. Grossman (excellent book, by the way), but the way he describes resonance is confusing me. I feel like the more I think about it, the more confusing it gets.

Consider a carbon-carbon double bond: C=C. He says that there are a few different ways that the pi electrons can be distributed in this bond:

C=C
(-)C--C(+)
(+)C--C(-)
.C--C.

Where the last structure is a radical. Although some of those structures are theoretically possible, they would offer a poor description of the behavior of the C=C . So, he develops a set of rules for which theoretical contributing structures are higher in energy and thus poorer descriptions of the chemical behavior.

So my question is, is this definition of "higher energy" a literal definition? Or am I misunderstanding the definition of resonance: degenerate solutions for the energy term in the Schrodinger equation--i.e., of equal energy!

If he is using an isolated double bond to describe resonance it is only being used in the form of an object lesson. ie. you might draw a double bond in the following ways...
just as you might draw resonance structures in the following ways. How the energies of the various representations are calculated, if not discussed by Grossman, can be assumed to be by one of the various MO methods that are accurate enough to provide a relative ranking.

The different structures correspond best to a set of valence bond structures. You can now form a matrix representaiton of your molecular hamiltonian using these structures as a basis. The diagonal matrix elements will be the "energies" of the hypothetical isolated structures. The importance of a given structure in the real wavefunction of the molecule depends not only on tihs energy but also on the value of the non-diagonal matrix elements. However it is important that resonance is not restricted to structures of the same energy.
These concepts should be exposed in the books by Linus Pauling, or, on a more theoretical basis in the classic book "quantum chemistry" by Eyring Walter and Kimball.